Related papers: Dictionary Learning with Low-rank Coding Coefficie…
We propose a new cross-conv algorithm for approximate computation of convolution in different low-rank tensor formats (tensor train, Tucker, Hierarchical Tucker). It has better complexity with respect to the tensor rank than previous…
Transformer architectures have achieved remarkable success across language, vision, and multimodal tasks, and there is growing demand for them to address in-context compositional learning tasks. In these tasks, models solve the target…
This paper considers the completion problem for a tensor (also referred to as a multidimensional array) from limited sampling. Our greedy method is based on extending the low-rank approximation pursuit (LRAP) method for matrix completions…
In this paper, we study multi-dimensional image recovery. Recently, transform-based tensor nuclear norm minimization methods are considered to capture low-rank tensor structures to recover third-order tensors in multi-dimensional image…
Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Although there has…
Recently, low-rank tensor completion has become increasingly attractive in recovering incomplete visual data. Considering a color image or video as a three-dimensional (3D) tensor, existing studies have put forward several definitions of…
Existing tensor completion formulation mostly relies on partial observations from a single tensor. However, tensors extracted from real-world data are often more complex due to: (i) Partial observation: Only a small subset (e.g., 5%) of…
Subword tokenization is a commonly used input pre-processing step in most recent NLP models. However, it limits the models' ability to leverage end-to-end task learning. Its frequency-based vocabulary creation compromises tokenization in…
Neural language models process sequences of words, but the mathematical operations inside them are insensitive to the order in which words appear. Positional encodings are the component added to remedy this. Despite their importance,…
In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cost and high…
We propose a Deep Texture Encoding Network (Deep-TEN) with a novel Encoding Layer integrated on top of convolutional layers, which ports the entire dictionary learning and encoding pipeline into a single model. Current methods build from…
Low rank matrix and tensor completion problems are to recover the incomplete two and higher order data by using their low rank structures. The essential problem in the matrix and tensor completion problems is how to improve the efficiency.…
We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…
Sparse coding in learned dictionaries has been established as a successful approach for signal denoising, source separation and solving inverse problems in general. A dictionary learning method adapts an initial dictionary to a particular…
Low-rank tensor completion has been widely used in computer vision and machine learning. This paper develops a novel multi-modal core tensor factorization (MCTF) method combined with a tensor low-rankness measure and a better nonconvex…
We propose a modular framework for multi-relational learning via tensor decomposition. In our learning setting, the training data contains multiple types of relationships among a set of objects, which we represent by a sparse three-mode…
In this paper, we propose a new adaptive cross algorithm for computing a low tubal rank approximation of third-order tensors, with less memory and lower computational complexity than the truncated tensor SVD (t-SVD). This makes it…
Sequential data such as time series, video, or text can be challenging to analyse as the ordered structure gives rise to complex dependencies. At the heart of this is non-commutativity, in the sense that reordering the elements of a…
Using the matrix product state (MPS) representation of tensor train decompositions, in this paper we propose a tensor completion algorithm which alternates over the matrices (tensors) in the MPS representation. This development is motivated…
Higher-order low-rank tensors naturally arise in many applications including hyperspectral data recovery, video inpainting, seismic data recon- struction, and so on. We propose a new model to recover a low-rank tensor by simultaneously…